TABLE OF CONTENTS In this section, we will begin by presenting some properties of PN codes and then discuss the maximal length sequences, Gold codes, and orthogonal codes. Some preliminary information includes a discussion on Galois fields (GFs). A field is a set of elements in which we can do addition, subtraction, multiplication, and division without ever leaving the set. When this field contains a finite number of elements, it is a finite field, also known as Galois field [10]. Here we list some general statements.
GF(2 n) means there exists a Galois field of 2 n elements.
A polynomial with coefficients from a binary field, GF(2), is called a binary polynomial.
A binary polynomial p( x) of degree m is said to be irreducible if it is not divisible by any binary polynomial of degrees less than m and greater than 0.
An irreducible polynomial p( x) of degree m is said to be a primitive if the smallest positive integer n for which p( x) divides x n + 1 is n = 2 m ? 1. For example, p( x) = 1 + x + x 4 is a primitive polynomial because the smallest integer for which 1 + x + x 4 divides x n + 1 is n = 2 4 ? 1 = 15.
We...
